CS 354 Procedural Methods

CS 354
Procedural Methods
Mark Kilgard
University of Texas
April 3, 2012

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Today’s material
 In-class quiz
 On interaction lecture
 Lecture topic
 Project 2
 Procedural methods

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My Office Hours
 Tuesday, before class
 Painter (PAI) 5.35
 8:45 a.m. to 9:15
 Thursday, after class
 ACE 6.302
 11:00 a.m. to 12

 Randy’s office hours
 Monday & Wednesday
 11 a.m. to 12:00
 Painter (PAI) 5.33

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Last time, this time
 Last lecture, we discussed
 Project 2 on Programmable Shaders
 Interaction
 Event models
 Buffering frames
 This lecture
 Project 2 discussion
 Procedural methods for texturing and modeling
 Intermediate milestone for Project 2 due
 Had to first 2 shader tasks done
 Deadline was yesterday
 All shaders due Friday, April 6th

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On a sheet of paper
Daily Quiz • Write your EID, name, and date
• Write #1, #2, #3, #4 followed by its answer

 Multiple choice: Which one of  True or False: Tearing is a
these is not an interactive event display artifact that results
processing model? from unsynchronized buffer
swap or blit operations.
a) Batching
b) Polling
 Multiple choice: Triple
buffering can improve display
c) Event-driven update latency but suffers
from:
 True or False: GLUT a) Requiring additional buffer
programs receive events memory
through callback functions.
b) May render frames that
are never actually displayed
c) Both a) and b)
d) Neither a) nor b)

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Project 2
 Project is NOW available
 PDF + code to use
 Requirements
 Mostly writing GLSL shaders
 Small amount of C/C++ code
 Convert height map to normal map
 Implement NormalMap::computeNormal method
 Intermediate milestone
 Yesterday: Monday, April 2nd
 Submit snapshots and GLSL code for first two shaders
 Complete project
 Due Friday, April 6th
 All 10 shaders
 Embellish for additional credit

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Your Mission So Far
 You should now have these first two
shaders tasks implemented

Task 1: apply decal

Task 0: roll torus

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Procedurally Generating a
Torus from a 2D Grid

2D grid over (s,t)∈[0,1]
Tessellated torus

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GLSL Standard Library Routines
You’ll Need for Project 2
 texture2D—accesses a 2D texture through a sampler2D and a 2-component
texture coordinate set (s,t)
 textureCube—access a cube map with a samplerCube and a 3-component
texture coordinate set (s,t,r)
 normalize—normalizes a vector
 cross—computes a cross product of 2 vectors
 dot—computes a dot (inner) product of 2 vectors
 max—compute the maximum of two values
 reflect—compute a reflection vector given an incident vector and a normal
vector
 vec3—constructor for 3-component vector from scalars
 mat3—constructor for 3x3 matrix from column vectors
 *—matrix-by-vector or vector-by-matrix multiplication
 sin—sine trigonometric function
 cos—cosine trigonometric function
 pow—raise a number to a power, exponentiation (hint: specular)

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Coordinate Spaces for Project 2
 Parametric space
 2D space [0..1]x[0..1] for 2D patch
 Object space
 Transform the patch’s parametric space into a 3D space
containing a torus
 Has modeling transformation from object- to world-space
 World space
 Environment map is oriented in this space
 gluLookAt’s coordinates are in this space
 Surface space
 (0,0,1) is always surface normal direction
 Mapping from object space to surface space varies along torus
 Perturbed normal from normal map overrides (0,0,1) geometric
normal
 Eye space
 gluLookAt transforms world space to eye space

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Artist-driven
Content Generation
 Advantages
 Human artistic expression!
 Human-to-human user interface
 Polish
 Disadvantages
 Human-intensive
 Takes time to make lots of it
 Involved to change
 Data intensive

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Image-driven
Content Generation
 Advantages
 As easy as taking pictures
 Disadvantages
 Very data-intensive
 Calibrating cameras & correlating images
 Quite involved
image panorama
 Involved to edit

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Procedural
Texturing and Modeling
 Let programs generate content!
 Advantages
 Small programs → lots of content
 Compact storage requirements
 Easy to generate more content
 Disadvantages
 Hard to control exactly

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Iterated Functions
 Provides infinite detail

Example:
Fractal Mandelbrot set

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Generating Lots of Content
Procedurally

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L-Systems
 Developed by Aristid Lindenmayer
 Theoretical biologist
 Hence the L in L-System
 Concept
 Use a rewriting system to model growth and
morphology of biological organisms
 Components
 Axiom – initial state
 Generator – applied recursively
 Useful in non-biology contexts too
 Geology, man-made objects, etc.

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Sierpinski Gasket
Rule based:

Repeat n times. As n →∞
Area→0
Perimeter →∞
Not a normal geometric object

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Apply Sierpinski Gasket Rules
Recursively

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Snow Flake Curve

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Other Axioms & Generators

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Tree Generation

An axial tree Sample tree generated from
branching patterns

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Plant Generation Rules

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Stochastic L-systems
 Probabilistic

Stochastic L-systems can
generate natural variations

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More Plant Generation Rules

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Fractal Mountains

[Przemyslaw Prusinkiewicz & Mark Hammel, 1993]

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Different Fractal Mountains

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Domain-specific Procedural
Artistry Tools

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Trees Really Matter
 Commercial product SpeedTree specializes at
drawing realistic trees fast

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Biological Inspiration
 Pseudo-Darwinian animation evolution

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Procedural Generation of
Buildings
 Buildings have rules too
 Doors, windows, facades
 Consistency of style
 Instant Architecture
façade derivation…

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Procedural Generation of Cities!
 Cities are very detailed and complex
 CityGen
 But follow regular rules – roads, blocks, respecting
topography, etc.

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Particle Systems

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Particle Systems and
Their Equations
pi = (xi, yi zi)
vi = dpi /dt = pi‘ = (dxi /dt, dyi /dt , zi /dt)

m vi‘= fi
Hard part is defining force vector

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Force Vector
 Independent Particles
 Gravity
 Wind forces
 O(n) calulation
 Coupled Particles O(n)
 Meshes
 Spring-Mass Systems
 Coupled Particles O(n2)
 Attractive and repulsive forces
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Solution of Particle Systems
float time, delta state[6n], force[3n];
state = initial_state();
for(time = t0; time<final_time, time+=delta) {
force = force_function(state, time);
state = ode(force, state, time, delta);
render(state, time)
}

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Simple Forces
 Consider force on particle i
fi = fi(pi, vi)
 Gravity fi = g
gi = (0, -g, 0)
 Wind forces
 Drag
pi(t0), vi(t0)

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Attraction and Repulsion
 Inverse square law
f = -krd/|d|3
 General case requires O(n2) calculation
 In most problems, the drop off is such that
not many particles contribute to the forces
on any given particle
 Sorting problem: is it O(n log n)?

E. Angel and D. Shreiner: Interactive Computer Graphics 6E © Addison-Wesley 2012 37

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Noise Textures
 Invented by Ken Perlin
 Academy Award winning idea
 A texturing primitive
 Basis for “natural” looking textures and
phenomenon
 No memory/bandwidth requirements
 Computed on the fly; no “source image”
 No mapping problem
 Naturally 3D so not prone to “gift wrapping” issues
 Useful for range of applications and
effects

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What is Noise?
 Band-limited repeatable
pseudo-random function
 Domain: Rn
 Approximate to Gaussian filtered
random noise
 Implemented as a pseudo-
random spline
 On regular grid
Marble vase
generated with
Perlin noise

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Variations on Noise
 Use noise within other functions

turbulence

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Combining Noise Patterns
 Sum noise patterns
 As frequency doubles, amplitude halves

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Turbulence
 Simulate turbulence by generating noise at
different octaves (scales)

 Average those octaves:

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Generating Marble Pattern
 Start with sine pattern in solid texture

 Then add turbulence
 Looks like veins in marble

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Variations on Marble
 Scale the magnitude of the turbulence
displacing the sine pattern

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Wood Pattern
 Start with cylindrical pattern
 Compute sine of distance from center of cylinder
 Interpolate between dark and light brown color

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Irregular Wood Rings
 Now use small amount of turbulence to displace
the tree rings in the wood

 Much less turbulence than marble case
 To preserve the rings

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Irregular Wood Grain
 Also want turbulence in Z direction but scale it
back to preserve the grain

less turbulence in z

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Shading with
Marble and Wood

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Other Procedurally Modeled
Phenomenon
 Smoke
 Difficult for an artist to model
 Needs to billow and flow around objects

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Entire Book on
Procedural Techniques

David Ebert,
Ken Musgrave,
Darwyn Peachey,
Ken Perlin,
Steve Worley

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Next Class
 Next lecture
 Bezier curves
 How do we move smoothly and simply with control?
 Project 2
 Shading and lighting with GLSL
 Due Friday, April 6th

CS 354 Procedural Methods

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